What does the “arrow of time” stand for?

One hundred and thirty years after the work of Ludwig Boltzmann on the interpretation of the irreversibility of physical phenomena, and one century after Einstein's formulation of Special Relativity, we are still not sure what we mean when we talk of “time” or “arrow of time”. We shall try to show that one source of this difficulty is our tendency to confuse, at least verbally, time and becoming, i.e. the course of time and the arrow of time, two concepts that the formalisms of modern physics are careful to distinguish. The course of time is represented by a time line that leads us to define time as the producer of duration. It is customary to place on this time line a small arrow that, ironically, must not be confused with the “arrow of time”. This small arrow is only there to indicate that the course of time is oriented, has a well-defined direction, even if this direction is arbitrary. The arrow of time, on the other hand, indicates the possibility for physical systems to experience, over the course of time, changes or transformations that prevent them from returning to their initial state forever. Contrary to what the expression “arrow of time” suggests, it is therefore not a property of time itself but a property of certain physical phenomena whose dynamic is irreversible. By its very definition, the arrow of time presupposes the existence of a wellestablished course of time within which – in addition – certain phenomena have their own temporal orientation. We think that it is worthwhile to emphasize the difference between several issues traditionally subsumed under the label “the problem of the direction of time”. If the expressions “course of time”, “direction of time” and “arrow of time” were better defined, systematically distinguished from one another and always used in their strictest sense, the debate about time, irreversibility and becoming in physics would become clearer.